The union of independent USFs on ℤd is transient

Eleanor Archer; Asaf Nachmias; Matan Shalev; Pengfei Tang

doi:10.1214/24-ECP609

The union of independent USFs on ℤ^d is transient

Eleanor Archer, Asaf Nachmias, Matan Shalev, Pengfei Tang

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the union of two or more independent uniform spanning forests (USF) on ℤ^d with d ≥ 3 almost surely forms a connected transient graph. In fact, this also holds when taking the union of a deterministic everywhere percolating set and an independent ε-Bernoulli percolation on a single USF sample.

Original language	English
Article number	38
Pages (from-to)	1-8
Number of pages	8
Journal	Electronic Communications in Probability
Volume	29
DOIs	https://doi.org/10.1214/24-ECP609
State	Published - 2024

Keywords

percolation
stochastic domination
uniform spanning forest

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/24-ECP609

Cite this

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abstract = "We show that the union of two or more independent uniform spanning forests (USF) on ℤd with d ≥ 3 almost surely forms a connected transient graph. In fact, this also holds when taking the union of a deterministic everywhere percolating set and an independent ε-Bernoulli percolation on a single USF sample.",

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